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for Chapter 5.2I

Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid from the Boolean standpoint, valid from the Aristotelian standpoint, or invalid. Then, identify the mood and figure, and cross-check your answers with the tables of valid syllogisms found in Section

Section

All corporations that overcharge their customers are unethical businesses. Some unethical businesses are investor-owned utilities.

Therefore, some investor-owned utilities are corporations that overcharge their customers.

Sample Solution

Chapter:Problem:

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Step 1 of 3

The validity of a categorical syllogism is determined by its
mood and figure:

Consider the statement provided in the textbook:

Assume,

Customers (C)

Businesses (U)

Investor-owned utilities (I)

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Step 2 of 3

First test the syllogism for the Boolean standpoint.

From the table the mood and the figure of the categorical
syllogism are.

Venn diagram for Boolean standpoint is:

The conclusion here states that there is an X in the area where
I and C circles overlap. There is an X in I circle, but whether the
X is inside or outside C is not clear. The X is dangling on the
overlap area. Hence, the syllogistic form is invalid.

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Step 3 of 3

One necessary condition to evaluate from Aristotelian standpoint
is that both the premises should be universal.

Since only one of the premises is universal .Therefore, this
syllogism cannot be evaluated from Aristotelian
standpoint.